Translation:My little brother loves anime.
Good question. I don't know if Japan makes a distinction between Western / foreign cartoons and its own. I think it probably does. If so, we should accept "cartoons" to mean Western animation and "anime" to mean Japanese native animation. And I think that distinction is important because, just as people who like The Simpsons don't necessarily like anime, Japanese anime watchers might not like the various offerings of Matt Groening and Seth Macfarlane.
I looked that up several years ago, and, hilariously enough, turns out there's no such distinction in Japanese language nor culture. We see Japanese cartoons as something special and use a special word for them, separating them from all the other animated cartoons, while for the Japanese themselves they are simply cartoons. Maybe it's just me, but I think it's pretty funny.
Similar to an earlier comment asking about "likes ~ a lot", "really likes" requires modifying the word 好き with 本当に (ほんとうに) or すごく. There is a subtly different emphasis or strength compared to 大好き. For a translation, I probably would accept it, but for a learning exercise (which this is) I can understand why it's marked incorrect.